{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,11]],"date-time":"2026-06-11T00:11:49Z","timestamp":1781136709340,"version":"3.54.1"},"reference-count":22,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2006,5,19]],"date-time":"2006-05-19T00:00:00Z","timestamp":1147996800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2006,7]]},"DOI":"10.1007\/s00211-006-0684-z","type":"journal-article","created":{"date-parts":[[2006,5,18]],"date-time":"2006-05-18T14:46:39Z","timestamp":1147963599000},"page":"1-2","source":"Crossref","is-referenced-by-count":13,"title":["Spectral discretization of the vorticity, velocity and pressure formulation of the Navier\u2013Stokes equations"],"prefix":"10.1007","volume":"104","author":[{"given":"Mejdi","family":"Aza\u00efez","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christine","family":"Bernardi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Nejmeddine","family":"Chorfi","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2006,5,19]]},"reference":[{"key":"684_CR1","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1007\/s00791-003-0107-y","volume":"6","author":"Amara","year":"2004","unstructured":"Amara, M., Capatina-Papaghiuc, D., Chac\u00f3n-Vera, E., Trujillo, D.: Vorticity\u2013velocity\u2013pressure formulation for Navier\u2013Stokes equations. Comput. Vis. Sci. 6, 47\u201352 (2004)","journal-title":"Comput. Vis. Sci."},{"key":"684_CR2","doi-asserted-by":"crossref","unstructured":"Amara, M., Capatina-Papaghiuc, D., Trujillo, D.: Stabilized finite element method for Navier\u2013Stokes equations with physical boundary conditions, Math. Comput. (to appear)","DOI":"10.1090\/S0025-5718-07-01929-1"},{"key":"684_CR3","doi-asserted-by":"crossref","first-page":"1673","DOI":"10.1090\/S0025-5718-03-01615-6","volume":"73","author":"Amara","year":"2004","unstructured":"Amara, M., Chac\u00f3n-Vera, E., Trujillo, D.: Vorticity\u2013velocity\u2013pressure formulation for the Stokes problem. Math. Comput. 73, 1673\u20131697 (2004)","journal-title":"Math. Comput."},{"key":"684_CR4","unstructured":"Amoura, K., Bernardi, C., Chorfi, N.: Spectral element discretization of the vorticity, velocity and pressure formulation of the Stokes problem, submitted"},{"key":"684_CR5","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1002\/(SICI)1099-1476(199806)21:9<823::AID-MMA976>3.0.CO;2-B","volume":"21","author":"Amrouche","year":"1998","unstructured":"Amrouche, C., Bernardi, C., Dauge, M., Girault, V.: Vector potentials in three-dimensional nonsmooth domains. Math. Meth. Appl. Sci. 21, 823\u2013864 (1998)","journal-title":"Math. Meth. Appl. Sci."},{"key":"684_CR6","unstructured":"B\u00e8gue, C., Conca, C., Murat, F., Pironneau, O.: Les \u00e9quations de Stokes et de Navier\u2013Stokes avec des conditions aux limites sur la pression. In: Nonlinear Partial Differential Equations and their Applications, Coll\u00e8ge de France Seminar, Vol. IX, 1988, pp. 179\u2013264"},{"key":"684_CR7","doi-asserted-by":"crossref","unstructured":"Bernardi, C., Chorfi, N.: Spectral discretization of the vorticity, velocity and pressure formulation of the Stokes problem, SIAM J. Numer. Anal. (to appear)","DOI":"10.1137\/050622687"},{"key":"684_CR8","unstructured":"Bernardi, C., Dauge, M., Maday, Y.: Polynomials in the Sobolev world, Internal Report, Laboratoire Jacques-Louis Lions. Universit\u00e9 Pierre et Marie Curie 2003"},{"key":"684_CR9","unstructured":"Bernardi, C., Girault, V., Raviart, P.-A.: Incompressible Viscous Fluids and their Finite Element Discretizations (in preparation)"},{"key":"684_CR10","doi-asserted-by":"crossref","unstructured":"Bernardi, C., Maday, Y.: Spectral Methods. In the Handbook of Numerical Analysis V, P.G. Ciarlet, J.-L. Lions (eds.), North-Holland, 1997, pp. 209\u2013485","DOI":"10.1016\/S1570-8659(97)80003-8"},{"key":"684_CR11","first-page":"1","volume":"36","author":"Brezzi","year":"1980","unstructured":"Brezzi, F., Rappaz, J., Raviart, P.-A.: Finite dimensional approximation of nonlinear problems. Part I: Branches of nonsingular solutions, Numer. Math. 36, 1\u201325 (1980)","journal-title":"Part I: Branches of nonsingular solutions, Numer. Math."},{"key":"684_CR12","doi-asserted-by":"crossref","first-page":"365","DOI":"10.1002\/mma.1670120406","volume":"12","author":"Costabel","year":"1990","unstructured":"Costabel, M.: A remark on the regularity of solutions of Maxwell's equations on Lipschitz domains. Math. Meth. Appl. Sci. 12, 365\u2013368 (1990)","journal-title":"Math. Meth. Appl. Sci."},{"key":"684_CR13","unstructured":"Costabel, M., Dauge, M.: Espaces fonctionnels Maxwell: Les gentils, les m\u00e9chants et les singularit\u00e9s, unpublished"},{"key":"684_CR14","unstructured":"Costabel, M., Dauge, M.: Computation of resonance frequencies for Maxwell equations in non smooth domains. In: M. Ainsworth, P. Davies, D. Duncan, P. Martin and B. Rynne, (eds.) Topics in Computational Wave Propagation, Springer, 2004 pp. 125\u2013161"},{"key":"684_CR15","doi-asserted-by":"crossref","first-page":"1091","DOI":"10.1002\/mma.328","volume":"25","author":"Dubois","year":"2002","unstructured":"Dubois, F.: Vorticity\u2013velocity\u2013pressure formulation for the Stokes problem. Math. Meth. Appl. Sci. 25, 1091\u20131119 (2002)","journal-title":"Math. Meth. Appl. Sci."},{"key":"684_CR16","doi-asserted-by":"crossref","first-page":"1395","DOI":"10.1016\/j.matpur.2003.09.002","volume":"82","author":"Dubois","year":"2003","unstructured":"Dubois, F., Sala\u00fcn, M., Salmon, S.: Vorticity\u2013velocity\u2013pressure and stream function-vorticity formulations for the Stokes problem. J. Math. Pures. Appl. 82, 1395\u20131451 (2003)","journal-title":"J. Math. Pures. Appl."},{"key":"684_CR17","doi-asserted-by":"crossref","unstructured":"Girault, V., Raviart, P.-A.: Finite Element Methods for Navier\u2013Stokes Equations, Theory and algorithms. Springer, Berlin Heidelberg New York, (1986)","DOI":"10.1007\/978-3-642-61623-5"},{"key":"684_CR18","unstructured":"Grisvard, P.: Elliptic Problems in Nonsmooth Domains. Pitman (1985)"},{"key":"684_CR19","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/0045-7825(90)90016-F","volume":"80","author":"Maday","year":"1990","unstructured":"Maday, Y., R\u00f8nquist, E.M.: Optimal error analysis of spectral methods with emphasis on non-constant coefficients and deformed geometries. Comp. Meth. Appl. Mech. Engrg. 80, 91\u2013115 (1990)","journal-title":"Comp. Meth. Appl. Mech. Engrg."},{"key":"684_CR20","doi-asserted-by":"crossref","first-page":"315","DOI":"10.1007\/BF01396415","volume":"35","author":"N\u00e9d\u00e9lec","year":"1980","unstructured":"N\u00e9d\u00e9lec, J.-C.: Mixed finite elements in \u211d3. Numer. Math. 35, 315\u2013341 (1980)","journal-title":"Numer. Math."},{"key":"684_CR21","unstructured":"Salmon, S.: D\u00e9veloppement num\u00e9rique de la formulation tourbillon\u2013vitesse\u2013pression pour le probl\u00e8me de Stokes, Thesis, Universit\u00e9 Pierre et Marie Curie, Paris (1999)"},{"key":"684_CR22","doi-asserted-by":"crossref","first-page":"353","DOI":"10.1007\/BF02418013","volume":"110","author":"Talenti","year":"1976","unstructured":"Talenti, G.: Best constant in Sobolev inequality. Ann. Math. Pura ed Appl. 110 serie IV, 353\u2013372 (1976)","journal-title":"Ann. Math. Pura ed Appl."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-006-0684-z.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-006-0684-z\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-006-0684-z","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T16:22:39Z","timestamp":1558628559000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-006-0684-z"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,5,19]]},"references-count":22,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,7]]}},"alternative-id":["684"],"URL":"https:\/\/doi.org\/10.1007\/s00211-006-0684-z","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,5,19]]}}}